1. Technical Field
The present invention relates to data processing in general, and in particular to an apparatus for performing non-linear functions. Still more particularly, the present invention relates to a mixed-signal system for performing Taylor series function approximations.
2. Description of Related Art
Although differential equations having strong non-linearities can be solved by using digital computers, they can only be performed at a relatively slow speed because strong non-linearities tend to render numerical algorithms for solving differential equations “stiff,” which often demand smaller time steps. On the other hand, analog computers can process signals almost instantaneously, but analog computers have been limited to non-linear functions (such as multiplications, logarithms, sinusoids, and exponentials) that can be synthesized by conventional analog components. In addition, the range of values over which non-linear functions can be synthesized has been severely limited by the saturation of analog components. Thus, any implementations of non-linear functions with analog components have been restricted to specific non-linear functions over a relatively limited range of values.
Artificial neural networks (ANN) and fuzzy logic systems have been utilized to perform analog function approximations. ANNs can typically be trained to approximate analog functions. Fuzzy logic systems typically incorporate a rule-based approach to the solving of a control problem instead of attempting to model a system mathematically. But even though approximation methods using fuzzy logic systems show some promising results in performing analog function approximations, they are still hampered by the saturation of analog circuits.
Consequently, it would be desirable to provide an improved apparatus capable of performing non-linear function approximations over a wide range of values.